Abstract: This article describes a three-channel encoding of nucleotide sequences, and proper formulas for filtering and downsampling such encoded sequences for multi-scale signal analysis. With proper interpolation, the encoded sequences can be visualized as curves in three-dimensional space. The filtering uses Gaussian-like smoothing kernels, chosen so that all levels of the multi-scale pyramid (except the original curve) are practically free from aliasing artifacts and have the same degree of smoothing. With these precautions, the overall shape of the space curve is robust under small changes in the DNA sequence, such as single-point mutations, insertions, deletions, and shifts.